Field of the Invention
The present invention relates to a technique of correcting the distortion of an image when displaying or projecting an image on a curved surface.
Description of the Related Art
To correct the distortion of an image when an image is projected on a curved surface, there is known a method of storing coordinates (to be referred to as “deformed coordinates” hereinafter) on a curved surface that correspond to grid points obtained by dividing a screen, supplementing the deformed coordinates between the grid points, and deforming an image to be projected (Japanese Patent Laid-Open No. 2001-069434). According to this method, the smaller the interval between grid points is, the smoother image deformation can be performed.
However, the smaller the interval between grid points is, the larger the data amount of deformed coordinate information becomes, the procedure to set deformed coordinate data for many grid points takes a long time, and the operation for deforming an image becomes complicated. To solve this, there is conceivable a method of sampling several grid points, setting deformed coordinate data corresponding to the sampled grid points, performing interpolation processing on deformed grid point data representing curves between the sampled grid points, and setting the interpolated deformed grid point data at grid points between the sampled grid points. This method can simplify the procedure to set deformed coordinate data, and smooth the operation for deforming an image.
As one method for performing interpolation processing of a curve, a Bezier curve based on a Bezier function with a small calculation amount is used. In general, the Bezier curve needs to be set between a start point and terminal point serving as anchor points using, as an indicating point, a control point for adjusting a curve. However, the control point does not exist on a curve to be interpolated, so it is difficult to calculate a desired curve between the start point and the terminal point.
To solve this, the following quadratic Bezier curve calculation method is known. First, the midpoint of a line segment connecting a start point and a terminal point is obtained in a state in which three anchor points serving as the start point, intermediate point, and terminal point of a quadratic Bezier curve exist. Then, a control point is set at a position having point symmetry with the midpoint using the intermediate point as the center, and a curve passing through the three anchor points is calculated.
The problem of poor deformation accuracy arises when an image is deformed based on a curved surface (cylinder, sphere, or prism) obtained by applying a curve obtained by the above-mentioned quadratic Bezier curve calculation method to supplement deformed coordinates between grid points. For example, it is known that a visually recognizable error (0.1 pixels or more) is generated in many patterns, from a comparison between the coordinate values of an ideal curved surface, and the coordinate values of an interpolated curved surface to which a curve estimated by the quadratic Bezier curve calculation method is applied.